# On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions

Igor Bock; Ivan Hlaváček; Ján Lovíšek

Aplikace matematiky (1984)

- Volume: 29, Issue: 4, page 303-314
- ISSN: 0862-7940

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topBock, Igor, Hlaváček, Ivan, and Lovíšek, Ján. "On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions." Aplikace matematiky 29.4 (1984): 303-314. <http://eudml.org/doc/15360>.

@article{Bock1984,

abstract = {A control of the system of nonlinear Kármán's equations for a thin elastic plate with clamped edge is considered. The transversal loading plays the role of the control variable. The set of admissible controls is chosen in a way guaranteeing the unique solvability of the state function with respect to the control variable is proved. A disscussion of uniqueness of the optimal control and some necessary conditions of optimality are presented.},

author = {Bock, Igor, Hlaváček, Ivan, Lovíšek, Ján},

journal = {Aplikace matematiky},

keywords = {nonlinear Kármán equations; transversal loading; Dirichlet boundary conditions; Existence of optimal control; differentiability; state function; nonlinear Kármán equations; transversal loading; Dirichlet boundary conditions; Existence of optimal control; differentiability; state function},

language = {eng},

number = {4},

pages = {303-314},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions},

url = {http://eudml.org/doc/15360},

volume = {29},

year = {1984},

}

TY - JOUR

AU - Bock, Igor

AU - Hlaváček, Ivan

AU - Lovíšek, Ján

TI - On the optimal control problem governed by the equations of von Kármán. I. The homogeneous Dirichlet boundary conditions

JO - Aplikace matematiky

PY - 1984

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 29

IS - 4

SP - 303

EP - 314

AB - A control of the system of nonlinear Kármán's equations for a thin elastic plate with clamped edge is considered. The transversal loading plays the role of the control variable. The set of admissible controls is chosen in a way guaranteeing the unique solvability of the state function with respect to the control variable is proved. A disscussion of uniqueness of the optimal control and some necessary conditions of optimality are presented.

LA - eng

KW - nonlinear Kármán equations; transversal loading; Dirichlet boundary conditions; Existence of optimal control; differentiability; state function; nonlinear Kármán equations; transversal loading; Dirichlet boundary conditions; Existence of optimal control; differentiability; state function

UR - http://eudml.org/doc/15360

ER -

## References

top- P. G. Ciarlet P. Rabier, Les équations de von Kármán, Springer Verlag, Berlin 1980. (1980) Zbl0433.73019MR0595326
- J. L. Lions, Sur le contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles, Dunod, Gauthier-Villars 1968. (1968) Zbl0179.41801MR0244606
- L. A. Ljusternik V. I. Sobolev, The elements of functional analysis, (in Russian). Moskva, Nauka 1965. (1965) MR0209802
- J. Nečas, Les méthodes directes en théorie des équations elliptiques, Academia, Praha 1967. (1967) MR0227584

## Citations in EuDML Documents

top- Igor Bock, Ivan Hlaváček, Ján Lovíšek, On the optimal control problem governed by the equations of von Kármán. II. Mixed boundary conditions
- Igor Bock, Ivan Hlaváček, Ján Lovíšek, On the optimal control problem governed by the equations of von Kármán. III. The case of an arbitrary large perpendicular load

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